Thank you for your question and the link Joseph P. provided will not pertain to your model Kenmore dryer.
There are many different types of controls used in the Kenmore dryers and without having the model number of your Kenmore dryer I will not be able to know what type of controls it has.
Based on you symptom and details the likely failure could be a thermal fuse or broken belt. Some models will not start if it detects a broken belt. There could many other failures preventing your Kenmore dryer from starting too.
Reply with the model number and I will be happy to provide model specific troubleshooting assistance.